As it will be shown in a moment, the droplet dynamics exhibits (simultaneously) both sliding and rolling regimes. Since the interface is moved with the material velocity (recall equation (REF )), the mesh quality may be reduced after some time. Hence, we introduce a mesh quality test which is performed every five time steps: we test the mesh quality by evaluating the edge ratio \(q_e\)  and the aspect ratio \(q_a\) . The edge ratio of a single tetrahedron is defined as the ratio of its longest and shortest edge, and \(q_e\)  is the maximum value over all tetrahedrons in mesh. The aspect ratio of a single tetrahedron \(K\)  is the ratio of its longest edge \(h_{\textrm {max}}(K)\)  and the radius of an inscribed sphere \(r(K)\) , \(q_a(K)=h_{\textrm {max}}(K) / (2\sqrt{6}\;r(K))\) . The aspect ratio of the mesh is then the maximum value of \(q_a(K)\)  over all tetrahedrons \(K\) . The mesh adaptation criterion is then defined by: \(q_e>3\)  or \(q_a>4\) . In this case, an automatic mesh adaptation is performed with an aim of a uniform mesh with mesh parameter \(h=0.15\) , i.e. the aim is the mesh with the similar quality as the initial mesh. Automatic mesh adaptation is performed within FreeFem++ with a built in meshing tool Mmg ([1]}). Relative volume oscillations do not exceed the order of \(10^{-4}\)  throughout the whole simulation.
